Study of the heat equation in a symmetric conical type domain of ℝN+1
Arezkı Kheloufı, Boubaker‐Khaled Sadallah · Mathematical Methods in the Applied Sciences · 2013
This paper is devoted to the analysis of the N-space dimensional heat equation, subject to Cauchy–Dirichlet boundary conditions. The problem is set in a symmetric conical type domain. More precisely, we look for sufficient conditions on the lateral boundary of the domain, as weak as possible in order to obtain the maximal regularity of the solution in an anisotropic Hilbertian Sobolev space. For this purpose, the domain decomposition method is employed. Copyright © 2013 John Wiley & Sons, Ltd.